Digital PSAT Math Practice Question 299: Answer and Explanation

Question: 299

In the rectangle drawn above, what is the product of the lengths of the two diagonals, AD and BC?

• A. 50
• B. 52
• C. 625
• D. 676

Correct Answer: D

Explanation:

(D) To solve this problem, you need to find the length of each diagonal in the rectangle. Note that since this is a rectangle, the lengths of both diagonals will be the same, so you just need to find the length of one diagonal, say AD. Draw this diagonal (the line connecting points A and D) in your picture, as shown below:

Note that by drawing this line, you create a right triangle whose hypotenuse is the diagonal AD. So, you need to find the length of the hypotenuse. From the picture, two side lengths are 10 and 24. Note that 10 = 2(5) and 24 = 2(12), so this triangle is just a multiple of the special 5-12-13 triangle; in your case, the side lengths are two times the side lengths of the special triangle. So, the length of your hypotenuse is 2(13) = 26.

Alternatively, if you don't remember the special 5-12-13 triangle, you can always use the Pythagorean theorem to find the length of the hypotenuse. Since the hypotenuse is your diagonal, it follows that the length of each diagonal is 26. The problem asks for the product of the diagonals, so the answer is 26 × 26 = 676, which is choice (D).